Global and local isometry-invariant descriptor for 3D shape comparison and partial matching

In this paper, based on manifold harmonics, we propose a novel framework for 3D shape similarity comparison and partial matching. First, we propose a novel symmetric mean-value representation to robustly construct high-quality manifold harmonic bases on nonuniform-sampling meshes. Then, based on the manifold harmonic bases constructed, a novel shape descriptor is presented to capture both of global and local features of 3D shape. This feature descriptor is isometry-invariant, i.e., invariant to rigid-body transformations and non-rigid bending. After characterizing 3D models with the shape features, we perform 3D retrieval with a up-to-date discriminative kernel. This kernel is a dimension-free approach to quantifying the similarity between two unordered featuresets, thus especially suitable for our high-dimensional feature data. Experimental results show that our framework can be effectively used for both comprehensive comparison and partial matching among non-rigid 3D shapes.

[1]  Martial Hebert,et al.  On 3D shape similarity , 1996, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[2]  Sunil Arya,et al.  An optimal algorithm for approximate nearest neighbor searching fixed dimensions , 1998, JACM.

[3]  Mark Meyer,et al.  Implicit fairing of irregular meshes using diffusion and curvature flow , 1999, SIGGRAPH.

[4]  Andrew E. Johnson,et al.  Using Spin Images for Efficient Object Recognition in Cluttered 3D Scenes , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Mark Meyer,et al.  Discrete Differential-Geometry Operators for Triangulated 2-Manifolds , 2002, VisMath.

[6]  Edwin R. Hancock,et al.  Correspondence Matching with Modal Clusters , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Ron Kimmel,et al.  On Bending Invariant Signatures for Surfaces , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  Ali Shokoufandeh,et al.  Shock Graphs and Shape Matching , 1998, International Journal of Computer Vision.

[9]  Terry Caelli,et al.  An eigenspace projection clustering method for inexact graph matching , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Leonidas J. Guibas,et al.  The Earth Mover's Distance as a Metric for Image Retrieval , 2000, International Journal of Computer Vision.

[11]  Kai Hormann,et al.  Surface Parameterization: a Tutorial and Survey , 2005, Advances in Multiresolution for Geometric Modelling.

[12]  Neil A. Dodgson,et al.  Advances in Multiresolution for Geometric Modelling , 2005 .

[13]  Niklas Peinecke,et al.  Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids , 2006, Comput. Aided Des..

[14]  Thomas A. Funkhouser,et al.  Partial matching of 3D shapes with priority-driven search , 2006, SGP '06.

[15]  Yi Liu,et al.  Shape Topics: A Compact Representation and New Algorithms for 3D Partial Shape Retrieval , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[16]  Bruno Lévy,et al.  Laplace-Beltrami Eigenfunctions Towards an Algorithm That "Understands" Geometry , 2006, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06).

[17]  Alexander M. Bronstein,et al.  Rock, Paper, and Scissors: extrinsic vs. intrinsic similarity of non-rigid shapes , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[18]  Raif M. Rustamov,et al.  Laplace-Beltrami eigenfunctions for deformation invariant shape representation , 2007 .

[19]  Martha Elizabeth Shenton,et al.  Global Medical Shape Analysis Using the Laplace-Beltrami Spectrum , 2007, MICCAI.

[20]  Hao Zhang,et al.  A spectral approach to shape-based retrieval of articulated 3D models , 2007, Comput. Aided Des..

[21]  Chunhong Pan,et al.  Consistent Correspondence between Arbitrary Manifold Surfaces , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[22]  Trevor Darrell,et al.  The Pyramid Match Kernel: Efficient Learning with Sets of Features , 2007, J. Mach. Learn. Res..

[23]  Xiaohu Guo,et al.  Spectral mesh deformation , 2008, The Visual Computer.

[24]  Dimension Amnesic Pyramid Match Kernel , 2008, AAAI.

[25]  B. Prabhakaran,et al.  A robust spectral approach for blind watermarking of manifold surfaces , 2008, MM&Sec '08.

[26]  Bruno Lévy,et al.  Spectral Geometry Processing with Manifold Harmonics , 2008, Comput. Graph. Forum.

[27]  Radu Horaud,et al.  Articulated shape matching using Laplacian eigenfunctions and unsupervised point registration , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[28]  Martin Reuter,et al.  Hierarchical Shape Segmentation and Registration via Topological Features of Laplace-Beltrami Eigenfunctions , 2010, International Journal of Computer Vision.

[29]  Hongbin Zha,et al.  Model Transduction for Triangle Meshes , 2010, Journal of Computer Science and Technology.

[30]  Bruno Lévy,et al.  Spectral Mesh Processing , 2009, SIGGRAPH '10.

[31]  Ramsay Dyer,et al.  Spectral Mesh Processing , 2010, Comput. Graph. Forum.

[32]  Jitendra Malik,et al.  Shape matching and object recognition using shape contexts , 2010, 2010 3rd International Conference on Computer Science and Information Technology.